Arithmetical or arithmetic (algebraic) geometry is a field with a less elementary definition. After the advent of scheme theory it could reasonably be defined as the study of Alexander Grothendieck's schemes of finite type over the spectrum of the ring of integersZ. This point of view has been very influential for around half a century; it has very widely been regarded as fulfilling Leopold Kronecker's ambition to have number theory operate only with rings that are quotients of polynomial rings over the integers (to use the current language of commutative algebra). In fact scheme theory uses all sorts of auxiliary constructions that do not appear at all 'finitistic', so that there is little connection with 'constructivist' ideas as such. That scheme theory may not be the last word appears from continuing interest in the 'infinite primes' (the real and complex local fields), which do not come from prime ideals as the p-adic numbers do.

Arithmetical or arithmetic (algebraic) geometry is a field with a less elementary definition. After the advent of scheme theory it could reasonably be defined as the study of Alexander Grothendieck's schemes of finite type over the spectrum of the ring of integersZ. This point of view has been very influential for around half a century; it has very widely been regarded as fulfilling Leopold Kronecker's ambition to have number theory operate only with rings that are quotients of polynomial rings over the integers (to use the current language of commutative algebra). In fact scheme theory uses all sorts of auxiliary constructions that do not appear at all 'finitistic', so that there is little connection with 'constructivist' ideas as such. That scheme theory may not be the last word appears from continuing interest in the 'infinite primes' (the real and complex local fields), which do not come from prime ideals as the p-adic numbers do.

Latest News for: height function

(Picture. Getty) ... Dr Stanley Coren, a professor at the University of British Columbia says a dog’s tail movement serves the same function as a human smile. ‘The tail’s position, specifically the height at which it is held, can be considered a sort of emotional meter,’ he said in Psychology Today. ‘A middle height suggests the dog is relaxed. If the tail is held horizontally, the dog is attentive and alert ... Advertisement ... (Picture ... MORE ... MORE....

First off lets get into it logically by sliding behind the steering wheel and lo behold what you have is a terrific driving position – right seat height, good forward and peripheral vision with no blind spots by a recalcitrant A-pillar and perfect ergonomics given the class of car that it is ...There is a new design steering wheel with multi-function controls for the stereo operation mounted on it....

Surprisingly, these “weak ties” (that funny colleague, for example) can serve important functions such as boosting physical and psychological health and buffering against stress and loneliness, researchers have found ... After controlling for age, education, sex, weight and height, the researchers found that the more social roles people engaged in, the better their lung function four years later....

While the player won’t quite reach the heights of its well-reviewed predecessor, the UBP-X800, it still packs in a sizeable amount of functionality for those looking to enhance their home cinema experience ... While that functionality has been scrapped again for the cheaper UBP-X500 model, you’re still able to play DolbyAtmos audio through your speakers....

The unveiling of Thiruvalluvar statue near Ulsoor lake in Bengaluru was significant since it was under the veil for nearly 18 years after the riots that reportedly targeted Tamils in the city at the height of the Cauvery agitation in the early 90s. Karunanidhi had then taken a vow not to attend any public function in Bengaluru until the Thiruvalluvar statue was unveiled. “We two brothers have set a precedent ...George ... ....

Lemon Laine, a natural beauty and wellness shop in Nashville, Tenn., will open a store in Heights Mercantile this fall ...Similar to the original store, founder and CEOLaura Lemon will offer a range of local and national products organized by use and function instead of by brand ... Heights Mercantile developer talks about what makes a Houston shopping center 'cool'....

It was the highest price paid of the nine multitenant warehouse sales here the past year ... • Bulk warehouse, ceiling clear height of 24 feet or more ... "In a market of this size, this difference can be a function of one or two medium-sized vacancies.". • Flex space, ceiling clear height less than 18 feet, generally ... • Service warehouse, ceiling clear height 18 to 24 feet, plus some shorter but functionally obsolete properties ... Richard Mize ... ....

Unlike glass-covered flexible displays, the new device can continue to function even after severe impacts, according to the Korean tech giant ... In tests based on US military standards, the device was dropped 26 times in succession from a height of 1.2 metres, with no loss of function. The screen was then dropped from a height of 1.8 metres and subjected to extreme temperature variation, yet still remained undamaged ... ....

The screen has been certified by Underwriters Laboratories, a testing firm for the US occupational safety and health administration, after tests that involved being dropped 26 times from a height of 1.2m, Samsung Display said. After testing, the screen continued to function normally, with no damage to its front, sides or edges, the firm said ... Reuters ....

Samsung Display, an Apple Inc supplier, said the screen can be used in devices such as smartphones, tablet computers, portable gaming machines and consoles in automobiles ...Occupational Safety and Health Administration, after tests which involved being dropped 26 times from a height of 1.2 metres, Samsung Display said. After testing, the screen continued to function normally, with no damage to its front, sides or edges, the firm said ... ....